ORBi Collection: Mathematics
http://hdl.handle.net/2268/153
The Collection's search engineSearch this channelsearch
http://orbi.ulg.ac.be/simple-search
Mathématique pour économistes et gestionnaires
http://hdl.handle.net/2268/197379
Title: Mathématique pour économistes et gestionnaires
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 12:09:06 GMTMathématique pour économistes et gestionnaires
http://hdl.handle.net/2268/197378
Title: Mathématique pour économistes et gestionnaires
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 12:06:13 GMTMathématique pour économistes et gestionnaires
http://hdl.handle.net/2268/197377
Title: Mathématique pour économistes et gestionnaires
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 11:59:57 GMTMathématique pour économistes et gestionnaires
http://hdl.handle.net/2268/197376
Title: Mathématique pour économistes et gestionnaires
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 11:56:47 GMTLoteries, combinatoire et heuristique
http://hdl.handle.net/2268/197367
Title: Loteries, combinatoire et heuristique
<br/>
<br/>Author, co-author: Breny, Henri; Esch, LouisThu, 26 May 2016 11:01:56 GMTUne propriété des matrices d'intensité utile dans la résolution des équations de Kolmogorov
http://hdl.handle.net/2268/197365
Title: Une propriété des matrices d'intensité utile dans la résolution des équations de Kolmogorov
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 10:56:45 GMTSur l'estimation ergodique du temps moyen de présence dans une file d'attente du type BMi/G/1
http://hdl.handle.net/2268/197363
Title: Sur l'estimation ergodique du temps moyen de présence dans une file d'attente du type BMi/G/1
<br/>
<br/>Author, co-author: Esch, LouisThu, 26 May 2016 10:51:42 GMTThe sequential analogue of the hypergeometric law
http://hdl.handle.net/2268/197326
Title: The sequential analogue of the hypergeometric law
<br/>
<br/>Author, co-author: Esch, LouisWed, 25 May 2016 13:58:45 GMTUn théorème de la théorie de la mesure
http://hdl.handle.net/2268/197321
Title: Un théorème de la théorie de la mesure
<br/>
<br/>Author, co-author: Esch, LouisWed, 25 May 2016 13:28:23 GMTModèles stochastiques de la thrombocytopoïèse
http://hdl.handle.net/2268/197263
Title: Modèles stochastiques de la thrombocytopoïèse
<br/>
<br/>Author, co-author: Esch, LouisTue, 24 May 2016 09:50:55 GMTLe problème du sous-espace invariant
http://hdl.handle.net/2268/197108
Title: Le problème du sous-espace invariant
<br/>
<br/>Author, co-author: Demeulenaere, Loïc
<br/>
<br/>Abstract: La présentation débute par la définition du problème du sous-espace invariant. Après quelques cas simples, elle aborde l'historique de ce problème et donne plusieurs résultats déjà connus.
<br/>
<br/>Commentary: Il s'agit d'un compte-rendu présenté lors d'un séminaire d'Analyse et concernant un sujet abordé par Etienne Matheron lors du congrès organisé en l'honneur des 60 ans de Gilles Godefroid (Mons, 4 et 5 novembre 2013).Fri, 20 May 2016 15:01:53 GMTDiametral Dimension of topological vector spaces
http://hdl.handle.net/2268/197097
Title: Diametral Dimension of topological vector spaces
<br/>
<br/>Author, co-author: Demeulenaere, Loïc
<br/>
<br/>Abstract: We present the definition and the main properties of the diametral dimension. We give an application to prove that two spaces are non-isomorphic. We also consider the case of Snu spaces.Fri, 20 May 2016 13:45:52 GMTImplementing and Comparing Stochastic and Robust Programming
http://hdl.handle.net/2268/197090
Title: Implementing and Comparing Stochastic and Robust Programming
<br/>
<br/>Author, co-author: Cuvelier, Thibaut
<br/>
<br/>Abstract: Traditional optimisation tools focus on deterministic problems: scheduling airline flight crews (with as few employees as possible while still meeting legal constraints, such as maximum working time), finding the shortest path in a graph (used by navigation systems to give directions, usually based on GPS signals), etc.
However, this deterministic hypothesis sometimes yields useless solutions: actual parameters cannot always be known to full precision, one reason being their randomness. For example, when scheduling trucks for freight transportation, if there is unexpected congestion on the roads, the deadlines might not be met, the company might be required to financially compensate for this delay, but also for the following deliveries that could not be made on schedule.
Two main approaches are developed in the literature to take into account this uncertainty: take decision based on probability distributions of the uncertain parameters (stochastic programming) or considering they lie in some set (robust programming). In general, the first one leads to a large increase in the size of the problems to solve (and thus requires algorithms to work around this dimensionality curse), while the second is more conservative but tends to change the nature of the programs (which can impose a new solver technology).
Some authors [2] claim that those two mindsets are equivalent, meaning that the solutions they provide are equivalent when faced with the same uncertainty. The goal of this thesis is to explore this question: for various problems, implement those two approaches, and compare them.
Is one solution more secluded from variations due to the uncertain parameters?
Does it bring benefits over a deterministic approach?
Is one cheaper than the other to compute?Fri, 20 May 2016 11:59:57 GMTOptimisation and uncertainty: comparing stochastic and robust programming
http://hdl.handle.net/2268/197081
Title: Optimisation and uncertainty: comparing stochastic and robust programming
<br/>
<br/>Author, co-author: Cuvelier, Thibaut
<br/>
<br/>Abstract: Traditional optimisation tools focus on deterministic problems: scheduling airline flight crews (with as few employees as possible while still meeting legal constraints, such as maximum working time), finding the shortest path in a graph (used by navigation systems to give directions), etc.
However, this deterministic hypothesis sometimes provides useless solutions: actual parameters cannot always be known to full precision, one reason being their randomness. For example, when scheduling trucks for freight transportation, if there is unexpected congestion on the roads, the deadlines might not be met, the company might be required to financially compensate for this delay, but also for the following deliveries that could not be made on schedule.
Two main approaches are developed in the literature to take into account this uncertainty: make decision based on probability distributions of the uncertain parameters (stochastic programming) or considering they lie in a so-called ¿uncertainty set¿ (robust programming). In general, the first one leads to a large increase in the size of the problems to solve (and thus requires algorithms to work around this dimensionality curse), while the second is more conservative but tends to change the nature of the programs (which can impose a new solver technology). This talk compares the two approaches on three different cases: facility location, unit-commitment, and reservoir management.
On the implementation side, multiple specific algorithms have been implemented to solve stochastic programs in order to compare their relative performance: Benders¿ decomposition, progressive hedging, and the deterministic equivalent. When comparing stochastic and robust programming, many differences appear in many aspects, even though the literature about those is very scarce. (Furthermore, those two approaches are not incompatible: both can be used in the same optimisation model to take into account different parts of the uncertainty.)
Concerning solving time, stochastic programming quickly gives rise to intractable problems, which requires the development of more specific algorithm just to be able to solve them to an acceptable accuracy in decent time. What is more, the stochastic description of the uncertain values (with a discretisation of the probability distribution through scenarios) must cover all the possible uncertainty, otherwise the solution risks overfitting those scenarios, and is likely to have poor performance on close but different scenarios that may happen in practice ¿ which imposes to use a large number of scenarios, which yields very large (and hardly tractable) optimisation programs.
On the other hand, by using specific uncertainty sets, robust programming yields programs that are only very slightly harder to solve, with an objective function that is very close to that of stochastic programming, but with totally different robustness properties: by using an uncertainty set computed from the scenarios, and not the scenarios themselves, it is able to withstand a much higher uncertainty than stochastic programming. However, when facing other types of uncertainty, this conclusion might turn untrue, with robust programming unable to cope with them and to bring interesting solutions to the table.Fri, 20 May 2016 10:44:56 GMTExtrait d'une lettre adressée à M. Hermite
http://hdl.handle.net/2268/197017
Title: Extrait d'une lettre adressée à M. Hermite
<br/>
<br/>Author, co-author: Catalan, EugèneThu, 19 May 2016 12:36:14 GMTDémonstration d'une propriété sur les courbes (solution de la question 311)
http://hdl.handle.net/2268/197009
Title: Démonstration d'une propriété sur les courbes (solution de la question 311)
<br/>
<br/>Author, co-author: Catalan, EugèneThu, 19 May 2016 11:26:56 GMTRemarque sur une note de M. Latars
http://hdl.handle.net/2268/197000
Title: Remarque sur une note de M. Latars
<br/>
<br/>Author, co-author: Catalan, EugèneThu, 19 May 2016 09:39:17 GMTUne généralisation du triangle de Pascal
http://hdl.handle.net/2268/196910
Title: Une généralisation du triangle de Pascal
<br/>
<br/>Author, co-author: Stipulanti, Manon; Rigo, Michel; Leroy, Julien
<br/>
<br/>Abstract: We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1]×[0, 1] associated with this extended Pascal triangle modulo a prime p.Tue, 17 May 2016 09:11:09 GMTUne généralisation du triangle de Pascal et la suite A007306
http://hdl.handle.net/2268/196909
Title: Une généralisation du triangle de Pascal et la suite A007306
<br/>
<br/>Author, co-author: Stipulanti, Manon
<br/>
<br/>Abstract: We introduce a generalization of Pascal triangle based on bino- mial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1]×[0, 1] associated with this extended Pascal triangle modulo a prime p. We consider a sequence (S(n))n≥0 counting the number of positive entries on each row of the generalized Pascal triangle. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥0, we prove that the sequence is 2-regular, give a linear representation and make the connection with the sequence of denominators occurring in the Farey tree.Tue, 17 May 2016 09:03:17 GMTGeneralized Pascal triangle for binomial coefficients of finite words
http://hdl.handle.net/2268/196908
Title: Generalized Pascal triangle for binomial coefficients of finite words
<br/>
<br/>Author, co-author: Stipulanti, Manon; Leroy, Julien; Rigo, Michel
<br/>
<br/>Abstract: Abstract. We introduce a generalization of Pascal triangle based on bino- mial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p.Tue, 17 May 2016 08:57:38 GMT